Family Riddle: How Many Brothers and Sisters?

How many brothers and sisters are there in the family?

In a family, a girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. Can you figure out how many brothers and sisters are in the family?

Choices:

A. 4 daughters and 3 sons

B. 3 daughters and 4 sons

C. 2 daughters and 5 sons

D. 5 daughters and 2 sons

Answer:

4 daughters and 3 sons

When faced with a riddle involving the number of brothers and sisters in a family, it's important to carefully consider the relationships between siblings. In this particular riddle, we are given the information that a girl has as many brothers as sisters, and each brother has only half as many brothers as sisters.

To solve this riddle, we can set up equations based on the relationships provided. Let's denote the number of daughters as D and the number of sons as S. We know that D = S, and each brother has half as many brothers as sisters, so each brother sees D/2 sisters and D brothers.

From the reference frame of one of the sisters, there are n sisters and n brothers. However, from the reference frame of a parent, we see the sister did not include herself in the counting. This means that there are n boys and n+1 girls.

From the reference frame of one of the brothers, there are n-1 brothers (since he wouldn’t count himself), and n+1 sisters. Each brother sees k brothers and 2k sisters. By combining these deductions, we can derive the equation 2(n-1) = n+1. Solving this equation gives us n=3.

Therefore, the final answer to the riddle is that there are 3 brothers and 4 sisters in the family.